# Distribution of perfect powers: parabolic sections

zak seidov zakseidov at yahoo.com
Thu Feb 21 22:18:55 CET 2008

```For those interested, relevant A's:

A097054 Non-square perfect powers.

A097055 Numbers n such that the interval n^2<x<(n+1)^2
contains at least one non-square perfect power

A097056 Numbers n such that the interval n^2<x<(n+1)^2
contains two or more distinct non-square perfect
powers A097054.

zak

--- zak seidov <zakseidov at yahoo.com> wrote:

> Distribution of perfect powers A001597 has an
> interesting pattern:
> there are many (rather long) runs with
> the constant second difference equal to 2.
>
> The longest such run (among first 10000 terms) is
> A001597(9697..9759) with 63 terms.
>
> These terms are (naturally)
> the squares of subsequent integers (9230..9292),
> of which one itself is perfect power, 9261=21^3.
>
> Are there longer runs of perfect squares,
> "not allowing other perfect powers between them"?
>
> thanks, zak
>
>
>
>
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